Asian Options Pricing Under The Double Heston Stochastic Volatility Model

Options are an important type of investment tool in the financial trading market.They are tools for both hedging and effective management of risk in modern financial markets.Therefore,option pricing is one of the hotspots and key points in financial research.With the continuous development of the financial market,the financial market continues to prosper and develop a variety of new options.Asian option is one of the most frequently traded exotic options in the financial market,and it is a strong path-dependent option.Compared with the standard option,the price is relatively low and the risk is small,which can effectively avoid man-made manipulation and control market risks,and also has significant effective hedging function.Therefore,Asian option is favored by investors and widely used in the real financial market.Because the classic Black-Scholes model is insufficient in portraying the behavior of the basic asset price movement in the financial market,and a lot of financial empirical analysis shows that the yield distribution of the basic asset price in the market has characteristics such as peak thick tail,volatility ”smiling” phenomenon,aggregation,and leverage effect.In order to explain the phenomenon of the real market,scholars constantly improve the Black-Scholes model and introduce models of different options.For example,stochastic volatility model,stochastic interest rate model,etc.Stochastic volatility model can capture the dynamics of financial market volatility and the combination of characteristics and volatility is widely used.The stochastic interest rate model can deduct various sources of uncertainty in interest rate variables.Additional state variables(such as inflation rate,GDP,etc.)can significantly improve the fitness of the model.Because multi-factor models can better describe interest rate uncertainty and dynamic characteristics of volatility,Good fit to financial market movements.In recent years,scholars have considered multi-factor models to build models for option pricing in light of the complex and changeable characteristics of the real market.This paper applies two Cox-Ingersoll-Ross models to describe the volatility of the underlying assets,and divides the volatility into two parts: long-term and short-term volatility.And examines the two arbitrary fluctuation factors of the stochastic interest rate,which can be expressed as the inflation rate and GDP composition,constructing a random interest rate and two-factor stochastic volatility model framework for Asian option pricing.Such models can better capture the dynamic characteristics of volatility changes and the term structure of interest rates,thus making the results of Asian option pricing closer to reality.Complex and volatile financial market.This paper uses the It?o formula,multi-dimensional random variable joint eigenfunction,partial differential equation,Gisanov measure transform and inverse Fourier transform technique to derive the continuous time case.The approximate display solution of the geometric Asian option price of the fixed execution price and the floating execution price,and the numerical example analysis is used to approximate the correctness and validity of the solution and the fixed execution price geometric Asian option is affected by the model parameters.Further,the arithmetic average price does not obey the lognormal distribution,and there is generally no closed-form pricing formula.Here,the Edgeworth approximation method is used to select the lognormal distribution approximation real distribution and the mathematical stochastic integration method to calculate the fixed arithmetic Asian options in continuous time.The average Asian option pricing is approximate analytical,and numerical examples are used to analyze the effect of fixed execution price arithmetic Asian options on model parameters.Numerical analysis shows that stochastic volatility and stochastic interest rate have a significant impact on option prices,especially for long-term options.The model is suitable for long-term actual market change modeling and credit risk management.Under the model,the Asian option pricing problem of continuous time case can simulate the complex and volatile financial market,enrich the theoretical system and numerical method of Asian option pricing,and provide more theoretical basis and method for the study of Asian options.At the same time,it also provides investors with reasonable risk assessment and hedging basis to obtain income.